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Q.

The equation of a plane which passes through the point of intersection of lines x−13=y−21=z−32 and x−31=y−12=z−23 and at greatest distance from point (0, 0, 0) is

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a

4x+3y+5z=25

b

4x+3y=5z=50

c

3x+4y+5z=49

d

x+7y−5z=2

answer is B.

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Detailed Solution

Let a point (3λ+1,λ+2,2λ+3)  of the first line also lies on the second line. Then Hence, the point of intersection P of the two lines is (4, 3, 5).Equation of plane perpendicular to OP, where O is (0, 0, 0), and passing through P is  4x+3y=5z=50
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